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Markov Properties for Linear Causal Models with Correlated Errors

Published: 01 June 2009 Publication History

Abstract

A linear causal model with correlated errors, represented by a DAG with bi-directed edges, can be tested by the set of conditional independence relations implied by the model. A global Markov property specifies, by the d-separation criterion, the set of all conditional independence relations holding in any model associated with a graph. A local Markov property specifies a much smaller set of conditional independence relations which will imply all other conditional independence relations which hold under the global Markov property. For DAGs with bi-directed edges associated with arbitrary probability distributions, a local Markov property is given in Richardson (2003) which may invoke an exponential number of conditional independencies. In this paper, we show that for a class of linear structural equation models with correlated errors, there is a local Markov property which will invoke only a linear number of conditional independence relations. For general linear models, we provide a local Markov property that often invokes far fewer conditional independencies than that in Richardson (2003). The results have applications in testing linear structural equation models with correlated errors.

Cited By

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  • (2016)Identification and overidentification of linear structural equation modelsProceedings of the 30th International Conference on Neural Information Processing Systems10.5555/3157096.3157274(1587-1595)Online publication date: 5-Dec-2016
  • (2016)Alternative Markov and causal properties for Acyclic Directed Mixed GraphsProceedings of the Thirty-Second Conference on Uncertainty in Artificial Intelligence10.5555/3020948.3021008(577-586)Online publication date: 25-Jun-2016
  • (2010)Introduction to Causal InferenceThe Journal of Machine Learning Research10.5555/1756006.185990511(1643-1662)Online publication date: 1-Aug-2010

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Published In

cover image The Journal of Machine Learning Research
The Journal of Machine Learning Research  Volume 10, Issue
12/1/2009
2936 pages
ISSN:1532-4435
EISSN:1533-7928
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JMLR.org

Publication History

Published: 01 June 2009
Published in JMLR Volume 10

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Cited By

View all
  • (2016)Identification and overidentification of linear structural equation modelsProceedings of the 30th International Conference on Neural Information Processing Systems10.5555/3157096.3157274(1587-1595)Online publication date: 5-Dec-2016
  • (2016)Alternative Markov and causal properties for Acyclic Directed Mixed GraphsProceedings of the Thirty-Second Conference on Uncertainty in Artificial Intelligence10.5555/3020948.3021008(577-586)Online publication date: 25-Jun-2016
  • (2010)Introduction to Causal InferenceThe Journal of Machine Learning Research10.5555/1756006.185990511(1643-1662)Online publication date: 1-Aug-2010

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